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A counting Bloom filter is a probabilistic data structure that is used to test whether the number of occurrences of a given element in a sequence exceeds a given threshold. As a generalized form of the Bloom filter, false positive matches are possible, but false negatives are not – in other words, a query returns either "possibly bigger or equal than the threshold" or "definitely smaller ...
One way to use the level-wise paradigm is to first discover all the frequent items in a level-wise fashion. It simply means counting the occurrences of all singleton elements in the database. Then, the transactions are filtered by removing the non-frequent items. At the end of this step, each transaction consists of only the frequent elements ...
The problem of finding the longest substring with at least occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and then finding the deepest node with at least leaf descendants. To avoid overlapping repeats, you can check that the list of suffix lengths has no consecutive ...
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
The simplicity of the counting sort algorithm and its use of the easily parallelizable prefix sum primitive also make it usable in more fine-grained parallel algorithms. [7] As described, counting sort is not an in-place algorithm; even disregarding the count array, it needs separate input and output arrays. It is possible to modify the ...
Counting filters provide a way to implement a delete operation on a Bloom filter without recreating the filter afresh. In a counting filter, the array positions (buckets) are extended from being a single bit to being a multibit counter. In fact, regular Bloom filters can be considered as counting filters with a bucket size of one bit.
For instance, if all occurrences of the letter e turn into the letter X, a ciphertext message containing numerous instances of the letter X would suggest to a cryptanalyst that X represents e. The basic use of frequency analysis is to first count the frequency of ciphertext letters and then associate guessed plaintext letters with them.
The products n(n − 1) count the number of combinations of n elements taken two at a time. (Actually this counts each pair twice; the extra factors of 2 occur in both numerator and denominator of the formula and thus cancel out.) Each of the n i occurrences of the i-th letter matches each of the remaining n i − 1 occurrences